论文标题
部分可观测时空混沌系统的无模型预测
On the Covers of Orbifold Curves Preserving the Slope Stability under Pullback
论文作者
论文摘要
我们完全表征了连接的Orbifold曲线的封面，这些曲线在回调形态下保留了向量束的斜率稳定性。更准确地说，给定覆盖$ f \ colon（y，q）\ longrightArrow（x，p）的连接的Orbifold曲线，我们表明，pushforward sheaf $ f _*\ Mathcal {O} _} _} _ {（y，q）_ {（y，q）$的最大不稳定子bundle $ coverinines the maximal coverines如果$ f $不通过任何非平凡的Étale子封面来考虑，封面$ f $就会真正受到打击。我们的主要结果指出，保留稳定捆绑包的$ f $的类别恰好是真正受损的覆盖$ f $的类。此外，我们为封面$ f $的封面建立了同等条件，以真正地被淘汰，从而将早期的作品推广到曲线封面上。我们彻底研究了Orbifold曲线上捆绑包的坡度稳定性条件，它们的特性在盖子下的推动力和回调图下，带有Deligne-Mumford堆栈的站点，从而为受试者奠定了坚实的基础。结果，我们还回答了真正受损的封面下稳定束的下降问题。
We completely characterize the covers of connected orbifold curves which preserve slope stability of vector bundles under the pullback morphism. More precisely, given a cover $f \colon (Y,Q) \longrightarrow (X,P)$ of connected orbifold curves, we show that the maximal destabilizing sub-bundle of the pushforward sheaf $f_*\mathcal{O}_{(Y,Q)}$ defines the maximal étale sub-cover of $f$. The cover $f$ is said to be genuinely ramified if $f$ does not factor through any non-trivial étale sub-cover. Our main result states that the class of covers $f$ that preserves the stable bundles under a pullback are precisely the class of genuinely ramified covers $f$. Further, we establish equivalent conditions for the cover $f$ to be genuinely ramified, generalizing earlier works on covers of curves. We thoroughly study the slope stability conditions of bundles on an orbifold curve, their properties under the pushforward and pullback maps under covers with a stand point of Deligne-Mumford stacks, hence giving a solid foundation of the subject. As a consequence, we also answer the question of descent of stable bundles under genuinely ramified covers.
